With recent advances in liquid crystal televisions, there are strong demands for the development of liquid crystal displays (hereinafter may be simply referred to as “LCDs”) capable of performing higher-speed switching. The present inventors have revealed that a flow effect of liquid crystal plays an important role in the LCD response (S. Onda, T. Miyashita, T. Uchida: Asia Display 98 Proceedings (1998) p. 1055). The theory of flow effect was developed by Ericksen-Leslie (F. M. Leslie: Quart. J. Mech, Appl. Math., 19 (1966) p. 357; F. M. Leslie: Liquid Crystals (1968) p. 365; and J. L. Ericksen: Mol. Cryst. Liq. Cryst. (1969) p. 153). According to this theory, based on the assumption that liquid crystal is an anisotropic viscous fluid, a fluid dynamical system incorporating the theory of continuous elastic bodies can be described by the equation of motion shown in Equation 1 and the conservation of angular momentum equation shown in Equation 2 (C. Z. van Doorn: J. of Applied Physics, 46, 9 (1975) p. 3738).
                                                [                  Equation          ⁢                                          ⁢          1                ]                                          Equation          ⁢                                          ⁢          of          ⁢                                          ⁢          Motion                ⁢                                  ⁢                                            ⅆ                              ⅆ                z                                      ⁢                          {                                                                                                                                            α                          2                                                ⁢                                                  n                          x                          &                                                ⁢                                                  n                          z                                                                    +                                                                        α                          3                                                ⁢                                                  n                          z                          &                                                ⁢                                                  n                          x                                                                    +                                                                                                                                                                                    (                                                                                                                    α                                1                                                            ⁢                                                              n                                x                                                            ⁢                                                              n                                y                                                            ⁢                                                              n                                z                                2                                                                                      +                                                                                          1                                2                                                            ⁢                                                              α                                3                                                            ⁢                                                              n                                x                                                            ⁢                                                              n                                y                                                                                      +                                                                                          1                                2                                                            ⁢                                                              α                                6                                                            ⁢                                                              n                                x                                                            ⁢                                                              n                                y                                                                                                              )                                                ⁢                                                                              ∂                                                          v                              y                                                                                                            ∂                            z                                                                                              +                                                                                                                                                                                    1                          2                                                ⁢                                                  (                                                                           ⁢                        2                        ⁢                                                  α                          1                                                ⁢                                                  n                          x                          2                                                ⁢                                                  n                          z                          2                                                                    -                                                                        α                          2                                                ⁢                                                  n                          z                          2                                                                    +                                                                        α                          3                                                ⁢                                                  n                          x                          2                                                                    +                                                                                                                                                          α                        4                                            +                                                                        α                          5                                                ⁢                                                  n                          z                          2                                                                    +                                                                        α                          6                                                ⁢                                                  n                          x                          2                                                ⁢                                                                             )                                                ⁢                                                                                                                              ⁢                                                                                                                                                                                                                                                                                                                                          ∂                                                                          v                                      x                                                                                                                                            ∂                                    z                                                                                                                                                                                                                                                                                      }                                =          0                ⁢                                  ⁢                                            ⅆ                              ⅆ                z                                      ⁢                          {                                                                                                                                            α                          2                                                ⁢                                                  n                          y                          &                                                ⁢                                                  n                          z                                                                    +                                                                        α                          3                                                ⁢                                                  n                          z                          &                                                ⁢                                                  n                          y                                                                    +                                                                                                                                                          (                                                                                                            α                              1                                                        ⁢                                                          n                              x                                                        ⁢                                                          n                              y                                                        ⁢                                                          n                              z                              2                                                                                +                                                                                    1                              2                                                        ⁢                                                          α                              3                                                        ⁢                                                          n                              x                                                        ⁢                                                          n                              y                                                                                +                                                                                    1                              2                                                        ⁢                                                          α                              6                                                        ⁢                                                          n                              x                                                        ⁢                                                          n                              y                                                                                                      )                                            ⁢                                                                        ∂                                                      v                                                                                                                                                      ⁢                              x                                                                                                                                ∂                          z                                                                                                                                                                                                                                  +                                                      1                            2                                                                          ⁢                                                  (                                                                           ⁢                        2                        ⁢                                                  α                          1                                                ⁢                                                  n                          y                          2                                                ⁢                                                  n                          z                          2                                                                    -                                                                        α                          2                                                ⁢                                                  n                          z                          2                                                                    +                                                                        α                          3                                                ⁢                                                  n                          y                          2                                                                    +                                                                                                                                                          α                        4                                            +                                                                        α                          5                                                ⁢                                                  n                          z                          2                                                                    +                                                                        α                          6                                                ⁢                                                  n                          y                          2                                                ⁢                                                                             )                                                ⁢                                                                              ∂                                                          v                              y                                                                                                            ∂                            z                                                                                                                                                          }                                =          0                                                
α1 to α6: Leslie viscosity coefficients
v: velocity vector
n: alignment vector
                                                [                  Equation          ⁢                                          ⁢          2                ]                                          Equation          ⁢                                          ⁢          of          ⁢                                          ⁢          Conservation          ⁢                                          ⁢          of          ⁢                                          ⁢          Angular          ⁢                                          ⁢          Momentum                ⁢                                  ⁢                                            γ              1                        ⁢                          n              x              &                                =                                    γ              ⁢                                                          ⁢                              n                x                                      -                                          ∂                F                                            ∂                                  n                  x                                                      +                                          ∂                                  ∂                  z                                            ⁢                                                ∂                  F                                                  ∂                                      (                                                                  ∂                                                  n                          x                                                                                            ∂                        z                                                              )                                                                        -                                          α                2                            ⁢                              n                z                            ⁢                                                ∂                                      v                    x                                                                    ∂                  z                                                                    ⁢                                  ⁢                                            γ              1                        ⁢                          n              y              &                                =                                    γ              ⁢                                                          ⁢                              n                y                                      -                                          ∂                F                                            ∂                                  n                  y                                                      +                                          ∂                                  ∂                  z                                            ⁢                                                ∂                  F                                                  ∂                                      (                                                                  ∂                                                  n                          y                                                                                            ∂                        z                                                              )                                                                        -                                          α                2                            ⁢                              n                z                            ⁢                                                ∂                                      v                    y                                                                    ∂                  z                                                                    ⁢                                  ⁢                                            γ              1                        ⁢                          n              z              &                                =                                    γ              ⁢                                                          ⁢                              n                z                                      -                                          ∂                F                                            ∂                                  n                  z                                                      +                                          ∂                                  ∂                  z                                            ⁢                                                ∂                  F                                                  ∂                                      (                                                                  ∂                                                  n                          z                                                                                            ∂                        z                                                              )                                                                        -                                          ɛ                0                            ⁢                                                Δɛ                  ⁡                                      (                                                                  D                        z                                                                                                                          n                            z                            2                                                    ⁡                                                      (                                                                                          ɛ                                //                                                            -                                                              ɛ                                ⊥                                                                                      )                                                                          +                                                  ɛ                          ⊥                                                                                      )                                                  2                            ⁢                              n                z                                      -                                          α                3                            ⁢                              n                x                            ⁢                                                ∂                                      v                    x                                                                    ∂                  z                                                      -                                          α                3                            ⁢                              n                y                            ⁢                                                ∂                                      v                    y                                                                    ∂                  z                                                                                                        γ1: rotational viscosity coefficient (γ1=α3−α2)    γ: arbitrary constant    Dz: electric flux density    ε//: permittivity along the major axis    ε⊥: permittivity along the minor axis    F: free energy density of distortion
  F  =                    1        2            ⁢                                    k            11                    ⁡                      (                                          Δ                //                            ⁢                              n                ρ                                      )                          2              +                  1        2            ⁢                                    k            22                    ⁡                      (                                                                                n                    ρ                                    //                                (                                  ▽                  ×                                      n                    ρ                                                  )                            +                              π                                  λ                  0                                                      )                          2              +                  1        2            ⁢                                    k            33                    (                                    n              ρ                        ×                          (                              ▽                ×                                  n                  ρ                                            )                                )                2            
k11, k22, k33: elastic constants
λ0: helical pitch
Coefficients α1 to α6 included in Equation 1 and Equation 2 described above are called Leslie viscosity coefficients. Since there is a relationship α6=α2+α3+α5 among these coefficients, five coefficients out of the total of six coefficients are independent. However, they cannot be directly measured in principle, as the correspondence with measuring systems is uncertain. On the other hand, Miesovicz viscosity coefficients are known as viscosity coefficients that are in a certain correspondence with measuring systems (that is, measurable in principle). As shown in FIG. 1, the Miesovicz viscosity coefficients include four coefficients, such as: viscosity coefficients η1 and η2 (shear viscosity coefficients) with respect to shear flows parallel to the minor axis and the major axis, respectively, of a molecule; a viscosity coefficient η3 (twist viscosity coefficient) with respect to flow in twist directions about the major axis of a molecule; and a viscosity coefficient η12 (compression viscosity coefficient) with respect to flow in directions along which the minor axis of a molecule is compressed. It is known that five parameters, including the rotational viscosity coefficient γ1 (this is also measurable) in Equation 2 in addition to the four viscosity coefficients described above, and the Leslie viscosity coefficients α1 to α6 have a relationship that can be expressed as shown in Equation 3. Therefore, if these five parameters can be measured with a high degree of accuracy, the Leslie viscosity coefficients can be determined by Equation 4 solving Equation 3 with respect to α. Using this result to solve Equation 1 and Equation 2 by computer numerical solution, a response of a liquid crystal can be properly evaluated, and further, a contribution to improved liquid crystal materials can be made.
η: Miesovicz viscosity coefficientη1=(−α2+α4+α5)/2η2=(α3+α4+α6)/2η3=α4/2η12=α1γ1=α3−α2  [Equation 3]α: Leslie viscosity coefficientα1=η12α2=−(η1−η2+γ1)/2α3=−(η1−η2−γ1)/2α4=2η3α5=(3η1+η2−4η3−γ1)/2(α6=α2+α3+α5)  [Equation 4]
A conventionally known method for measuring the viscosity coefficients of a liquid crystal is a method for determining the optimal parameters, using the electrical response characteristics of a twisted nematic (TN) liquid crystal cell, by fitting calculated values obtained by simultaneously varying the above-described five parameters to measured values (O. Cossalter, B. Carmer, D. A. Mlynsky: J. of Physics 2, At. Mol. Cluster Phys. Chem. Phys. Mech. Hydrodyn. Vol. 6, No. 12 (1996) pp. 1663-1669). Since the parameter η12 related to compression is generally negligible, the number of parameters that are simultaneously varied is normally four. As for the rotational viscosity coefficient γ1, there is a known measuring method using a rotational viscometer with a special structure, in which voltages can be applied to two movable surfaces (K. Skarp, S. T. Lagerwall, B. Stebler: “Measurement of hydrodynamic parameters for nematic 5CB”, Molecular Crystal Liquid Crystal, Vol. 60 (1980) pp. 215-236).